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Symmetries and turbulence modeling

Klingenberg, Dario ; Oberlack, Martin ; Plümacher, Dominik (2022)
Symmetries and turbulence modeling.
In: Physics of Fluids, 32
doi: 10.26083/tuprints-00011507
Artikel, Erstveröffentlichung, Verlagsversion

Kurzbeschreibung (Abstract)

This work applies new insights into turbulent statistics gained by Lie symmetry analysis to the closure problem of turbulence. Founded in the mathematics of partial differential equations, Lie symmetries have helped advances in many fields of modern physics. The main reason for this is their ability to encode important physical principles that are implicitly expressed by governing equations. Newly discovered symmetries of the multi-point correlation equations describing turbulentmotion have been shown to encode two central effects of turbulent statistics, intermittency and non- Gaussianity. Moreover, these symmetries play a pivotal role in obtaining turbulent scaling laws such as the logarithmic law of the wall. Evidently, correctly preserving these symmetry properties in a turbulencemodelwould render it capable of accurately predicting important effects of turbulent statistics and turbulent scaling. As these symmetry constraints have so far not been taken into account when devising turbulence models, we present a completely new modeling framework that can yield models fulfilling these conditions. In order to accomplish this, it turns out to be helpful, if not necessary, to introduce an entirely new symmetry-based modeling strategy that allows systematically constructing equations based on symmetry constraints imposed on them. From these considerations, it can be shown that in order to create meaningful turbulence models that fulfill these constraints, it is necessary to introduce a new velocity and pressure field. A possible skeleton of model equations for second-moment closure is presented.

Typ des Eintrags: Artikel
Erschienen: 2022
Autor(en): Klingenberg, Dario ; Oberlack, Martin ; Plümacher, Dominik
Art des Eintrags: Erstveröffentlichung
Titel: Symmetries and turbulence modeling
Sprache: Englisch
Publikationsjahr: 2022
Ort: Darmstadt
Titel der Zeitschrift, Zeitung oder Schriftenreihe: Physics of Fluids
Jahrgang/Volume einer Zeitschrift: 32
Kollation: 18 Seiten
DOI: 10.26083/tuprints-00011507
URL / URN: https://tuprints.ulb.tu-darmstadt.de/11507
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Kurzbeschreibung (Abstract):

This work applies new insights into turbulent statistics gained by Lie symmetry analysis to the closure problem of turbulence. Founded in the mathematics of partial differential equations, Lie symmetries have helped advances in many fields of modern physics. The main reason for this is their ability to encode important physical principles that are implicitly expressed by governing equations. Newly discovered symmetries of the multi-point correlation equations describing turbulentmotion have been shown to encode two central effects of turbulent statistics, intermittency and non- Gaussianity. Moreover, these symmetries play a pivotal role in obtaining turbulent scaling laws such as the logarithmic law of the wall. Evidently, correctly preserving these symmetry properties in a turbulencemodelwould render it capable of accurately predicting important effects of turbulent statistics and turbulent scaling. As these symmetry constraints have so far not been taken into account when devising turbulence models, we present a completely new modeling framework that can yield models fulfilling these conditions. In order to accomplish this, it turns out to be helpful, if not necessary, to introduce an entirely new symmetry-based modeling strategy that allows systematically constructing equations based on symmetry constraints imposed on them. From these considerations, it can be shown that in order to create meaningful turbulence models that fulfill these constraints, it is necessary to introduce a new velocity and pressure field. A possible skeleton of model equations for second-moment closure is presented.

Status: Verlagsversion
URN: urn:nbn:de:tuda-tuprints-115075
Sachgruppe der Dewey Dezimalklassifikatin (DDC): 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau
Fachbereich(e)/-gebiet(e): 16 Fachbereich Maschinenbau
16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy)
16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy) > Strömungsmechanische Modellentwicklung
16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy) > Turbulenz- und Verbrennungsforschung
Hinterlegungsdatum: 09 Nov 2022 14:03
Letzte Änderung: 10 Nov 2022 06:55
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